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Crystal structure on rigged configurations

Anne Schilling
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Abstract

Rigged configurations are combinatorial objects originating from the Bethe Ansatz, that label highest weight crystal elements. In this paper a new unrestricted set of rigged configurations is introduced for types ADE by constructing a crystal structure on the set of rigged configurations. In type A an explicit characterization of unrestricted rigged configurations is provided which leads to a new fermionic formula for unrestricted Kostka polynomials or q-supernomial coefficients. The affine crystal structure for type A is obtained as well.

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Anne Schilling. 2005-08-05. Crystal structure on rigged configurations. https://doi.org/10.1155/imrn/2006/97376

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